Leonin Arbiter

If an effect says "You may search your library . . . If you do, shuffle your library" or "You may search your library . . . then shuffle your library," you can't choose to search, so you won't shuffle.

If an effect says "Search your library . . . then shuffle your library," you shuffle you libraries even though you can't search.

Effects that instruct you to reveal or look at cards from the top of you library will still work. Only effects that use the word "search" are affected.

Once a player has paid {2}, they may search libraries that turn as many times as they are instructed to do so.

If there are multiple Leonin Arbiters on the battlefield, a player must pay {2} for each one before being able to search libraries that turn.

A player who has paid {2} may search any library when instructed to do so that turn, not just their own library.